Good idea. How would you put a door on this? I would think thin metal hinges would melt. What kind of latch / closure would hold up to heat?
Yes, steel outside the drywall would be subject to melting. One could use high-temp steel hinges (Inconel= $$) and put it on the outside, or use hinges that fit entirely internal (e.g European-style concealed hinges). The simplest approach is to just make a hatch/panel that clips into place using spring catches--all on the inside.
BTW: If functionality and "quick" is more important than looks, aluminum foil tape works well for dressing the edges of the drywall sheets for a project like this. AL foil stuck on the outside of the whole box will help reflect radiant heat, and AL foil on the inside of the box (if not in contact with the safe inside) will provide a low emissivity surface. All of this may buy a few additional minutes of safety for the contents.